On the structure and dynamics of water associated with single-supported zwitterionic and anionic membranes.

We have used high-resolution quasielastic neutron scattering (QENS) to investigate the dynamics of water molecules (time scale of motion ∼10-11-10-9 s) in proximity to single-supported bilayers of the zwitterioniclipid DMPC (1,2-dimyristoyl-sn-glycero-3-phosphorylcholine) and the anionic lipid DMPG (1,2-dimyristoyl-sn-glycero-3-phosphoglycerol) in the temperature range 160-295 K. For both membranes, the temperature dependence of the intensity of neutronsscattered elastically and incoherently from these samples indicates a series of freezing/melting transitions of the membrane-associated water, which have not been observed in previous studies of multilayer membranes. We interpret these successive phase transitions as evidence of different types of water that are common to the two membranes and which are defined by their local environment: bulk-like water located furthest from the membrane and two types of confined water in closer proximity to the lipids. Specifically, we propose a water type termed "confined 2" located within and just above the lipid head groups of the membrane and confined 1 water that lies between the bulk-like and confined 2 water. Confined 1 water is only present at temperatures below the freezing point of bulk-like water. We then go on to determine the temperature dependence of the translational diffusion coefficient of the water associated with single-supported DMPG membranes containing two different amounts of water as we have previously done for DMPC. To our knowledge, there have been no previous studies comparing the dynamics of water in proximity to zwitterionic and anionic membranes. Our analysis of the water dynamics of the DMPG and DMPC membranes supports the classification of water types that we have inferred from their freezing/melting behavior. However, just as we observe large differences in the freezing/melting behavior between these model membranes for the same water type, our measurements demonstrate variation between these membranes in the dynamics of their associated water over a wide temperature range. In particular, there are differences in the diffusive motion of water closest to the lipid head groups. Previously, QENS spectra of the DMPC membranes have revealed the motion of water bound to the lipid head groups. For the DMPG membrane, we have found some evidence of such bound water molecules; but the signal is too weak for a quantitative analysis. However, we observe confined 2 water in the DMPG membrane to undergo slow translational diffusion in the head group region, which was unobserved for DMPC. The weak temperature dependence of its translational diffusion coefficient allows extrapolation to physiological temperatures for comparison with molecular dynamics simulations.

Structure and dynamics of water and lipid molecules in charged anionic DMPG lipid bilayer membranes.

Molecular dynamics simulations have been used to investigate the influence of the valency of counter-ions on the structure of freestanding bilayer membranes of the anionic 1,2-dimyristoyl-sn-glycero-3-phosphoglycerol (DMPG) lipid at 310 K and 1 atm. At this temperature, the membrane is in the fluid phase with a monovalent counter-ion and in the gel phase with a divalent counter-ion. The diffusion constant of water as a function of its depth in the membrane has been determined from mean-square-displacement calculations. Also, calculated incoherent quasielastic neutron scattering functions have been compared to experimental results and used to determine an average diffusion constant for all water molecules in the system. On extrapolating the diffusion constants inferred experimentally to a temperature of 310 K, reasonable agreement with the simulations is obtained. However, the experiments do not have the sensitivity to confirm the diffusion of a small component of water bound to the lipids as found in the simulations. In addition, the orientation of the dipole moment of the water molecules has been determined as a function of their depth in the membrane. Previous indirect estimates of the electrostatic potential within phospholipid membranes imply an enormous electric field of 10(8)-10(9) V m(-1), which is likely to have great significance in controlling the conformation of translocating membrane proteins and in the transfer of ions and molecules across the membrane. We have calculated the membrane potential for DMPG bilayers and found ∼1 V (∼2 ⋅ 10(8) V m(-1)) when in the fluid phase with a monovalent counter-ion and ∼1.4 V (∼2.8 ⋅ 10(8) V m(-1)) when in the gel phase with a divalent counter-ion. The number of water molecules for a fully hydrated DMPG membrane has been estimated to be 9.7 molecules per lipid in the gel phase and 17.5 molecules in the fluid phase, considerably smaller than inferred experimentally for 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine (DMPC) membranes but comparable to the number inferred for 1,2-dilauroyl-sn-glycero-3-phosphoethanolamine (DLPE) membranes. Some of the properties of the DMPG membrane are compared with those of the neutral zwitterionic DMPC bilayer membrane at 303 K and 1 atm, which is the same reduced temperature with respect to the gel-to-fluid transition temperature as 310 K is for the DMPG bilayer membrane.

Atomic scattering from an adsorbed monolayer solid with a helium beam that penetrates to the substrate.

Diffraction and one-phonon inelastic scattering of a thermal energy helium atomic beam are evaluated in the situation that the target monolayer lattice is so dilated that the atomic beam penetrates to the interlayer region between the monolayer and the substrate. The scattering is simulated by propagating a wavepacket and including the effect of a feedback of the inelastic wave onto the diffracted wave, which represents a coherent re-absorption of the created phonons. Parameters are chosen to be representative of an observed p(1 × 1) commensurate monolayer solid of H2/NaCl(001) and a conjectured p(1 × 1) commensurate monolayer solid of H2/KCl(001). For the latter, there are cases where part of the incident beam is trapped in the interlayer region for times exceeding 50 ps, depending on the spacing between the monolayer and the substrate and on the angle of incidence. The feedback effect is large for cases of strong transient trapping.

Diffusion of water and selected atoms in DMPC lipid bilayer membranes.

Molecular dynamics simulations have been used to determine the diffusion of water molecules as a function of their position in a fully hydrated freestanding 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine (DMPC) bilayer membrane at 303 K and 1 atm. The diffusion rate of water in a ∼10 Šthick layer just outside the membrane surface is reduced on average by a factor of ∼2 relative to bulk. For water molecules penetrating deeper into the membrane, there is an increasing reduction in the average diffusion rate with up to one order of magnitude decrease for those deepest in the membrane. A comparison with the diffusion rate of selected atoms in the lipid molecules shows that ∼6 water molecules per lipid molecule move on the same time scale as the lipids and may therefore be considered to be tightly bound to them. The quasielastic neutron scattering functions for water and selected atoms in the lipid molecule have been simulated and compared to observed quasielastic neutron scattering spectra from single-supported bilayer DMPC membranes.

Calculation of inelastic helium atom scattering from H2/NaCl(001).

The one-phonon inelastic low energy helium atom scattering theory is adapted to cases where the target monolayer is a p(1 × 1) commensurate square lattice. Experimental data for para-H(2)/NaCl(001) are re-analyzed and the relative intensities of energy loss peaks in the range 6 to 9 meV are determined. The case of the H(2)/NaCl(001) monolayer for 26 meV scattering energy is computationally challenging and difficult because it has a much more corrugated surface than those in the previous applications for triangular lattices. This requires a large number of coupled channels for convergence in the wave-packet-scattering calculation and a long series of Fourier amplitudes to represent the helium-target potential energy surface. A modified series is constructed in which a truncated Fourier expansion of the potential is constrained to give the exact value of the potential at some key points and which mimics the potential with fewer Fourier amplitudes. The shear horizontal phonon mode is again accessed by the helium scattering for small misalignment of the scattering plane relative to symmetry axes of the monolayer. For 1° misalignment, the calculated intensity of the longitudinal acoustic phonon mode frequently is higher than that of the shear horizontal phonon mode in contrast to what was found at scattering energies near 10 meV for triangular lattices of Ar, Kr, and Xe on Pt(111).

Structure and phase transitions of monolayers of intermediate-length n-alkanes on graphite studied by neutron diffraction and molecular dynamics simulation.

We present evidence from neutron diffraction measurements and molecular dynamics (MD) simulations of three different monolayer phases of the intermediate-length alkanes tetracosane (n-C(24)H(50) denoted as C24) and dotriacontane (n-C(32)H(66) denoted as C32) adsorbed on a graphite basal-plane surface. Our measurements indicate that the two monolayer films differ principally in the transition temperatures between phases. At the lowest temperatures, both C24 and C32 form a crystalline monolayer phase with a rectangular-centered (RC) structure. The two sublattices of the RC structure each consists of parallel rows of molecules in their all-trans conformation aligned with their long axis parallel to the surface and forming so-called lamellas of width approximately equal to the all-trans length of the molecule. The RC structure is uniaxially commensurate with the graphite surface in its [110] direction such that the distance between molecular rows in a lamella is 4.26 A=sqrt[3a(g)], where a(g)=2.46 A is the lattice constant of the graphite basal plane. Molecules in adjacent rows of a lamella alternate in orientation between the carbon skeletal plane being parallel and perpendicular to the graphite surface. Upon heating, the crystalline monolayers transform to a "smectic" phase in which the inter-row spacing within a lamella expands by approximately 10% and the molecules are predominantly oriented with the carbon skeletal plane parallel to the graphite surface. In the smectic phase, the MD simulations show evidence of broadening of the lamella boundaries as a result of molecules diffusing parallel to their long axis. At still higher temperatures, they indicate that the introduction of gauche defects into the alkane chains drives a melting transition to a monolayer fluid phase as reported previously.

Enhanced creation of dispersive monolayer phonons in XePt(111) by inelastic helium atom scattering at low energies.

Conditions likely to lead to enhanced inelastic atomic scattering that creates shear horizontal (SH) and longitudinal acoustic (LA) monolayer phonons are identified, specifically examining the inelastic scattering of (4)He atoms by a monolayer solid of XePt(111) at incident energies of 2-25 meV. There is strong inelastic scattering for both dispersive phonon branches (SH and LA) of the monolayer at incident energies below 8 meV. Several improvements enable more complete wave packet calculations of the inelastic scattering than in previous work. Long propagation times are made feasible by adding an absorbing potential at large distance. The times now extend to beyond 100 ps and enable a clarification of processes involving transient trapping of the He atoms. The wave packet is made more monochromatic by significantly increasing the spatial width of the initial Gaussian shape. The narrower energy distribution in the incident beam then enables a demonstration of strong energy dependence of the scattering over a scale of less than 0.3 meV.

Comparative study of normal and branched alkane monolayer films adsorbed on a solid surface. I. Structure.

The structure of a monolayer film of the branched alkane squalane (C30H62) adsorbed on graphite has been studied by neutron diffraction and molecular dynamics (MD) simulations and compared with a similar study of the n-alkane tetracosane (n-C24H52). Both molecules have 24 carbon atoms along their backbone and squalane has, in addition, six methyl side groups. Upon adsorption, there are significant differences as well as similarities in the behavior of these molecular films. Both molecules form ordered structures at low temperatures; however, while the melting point of the two-dimensional (2D) tetracosane film is roughly the same as the bulk melting point, the surface strongly stabilizes the 2D squalane film such that its melting point is 91 K above its value in bulk. Therefore, squalane, like tetracosane, will be a poor lubricant in those nanoscale devices that require a fluid lubricant at room temperature. The neutron diffraction data show that the translational order in the squalane monolayer is significantly less than in the tetracosane monolayer. The authors' MD simulations suggest that this is caused by a distortion of the squalane molecules upon adsorption on the graphite surface. When the molecules are allowed to relax on the surface, they distort such that all six methyl groups point away from the surface. This results in a reduction in the monolayer's translational order characterized by a decrease in its coherence length and hence a broadening of the diffraction peaks. The MD simulations also show that the melting mechanism in the squalane monolayer is the same footprint reduction mechanism found in the tetracosane monolayer, where a chain melting drives the lattice melting.

Comparative study of normal and branched alkane monolayer films adsorbed on a solid surface. II. Dynamics.

The dynamics of monolayer films of the n-alkane tetracosane (n-C24H52) and the branched alkane squalane (C30H62) adsorbed on graphite have been studied by quasielastic and inelastic neutron scattering and molecular dynamics (MD) simulations. Both molecules have 24 carbon atoms along their carbon backbone, and squalane has an additional six methyl side groups symmetrically placed along its length. The authors' principal objective has been to determine the influence of the side groups on the dynamics of the squalane monolayer and thereby assess its potential as a nanoscale lubricant. To investigate the dynamics of these monolayers they used both the disk chopper spectrometer (DCS) and the high flux backscattering spectrometer (HFBS) at the National Institute of Standards and Technology. These instruments made it possible to study dynamical processes such as molecular diffusive motions and vibrations on very different time scales: 1-40 ps (DCS) and 0.1-4 ns (HFBS). The MD simulations were done on corresponding time scales and were used to interpret the neutron spectra. The authors found that the dynamics of the two monolayers are qualitatively similar on the respective time scales and that there are only small quantitative differences that can be understood in terms of the different masses and moments of inertia of the two molecules. In the course of this study, the authors developed a procedure to separate out the low-frequency vibrational modes in the spectra, thereby facilitating an analysis of the quasielastic scattering. They conclude that there are no major differences in the monolayer dynamics caused by intramolecular branching. It remains to be seen whether this similarity in monolayer dynamics also holds for the lubricating properties of these molecules in confined geometries.

Atomic force microscopy measurements of topography and friction on dotriacontane films adsorbed on a SiO2 surface.

We report comprehensive atomic force microscopy (AFM) measurements at room temperature of the nanoscale topography and lateral friction on the surface of thin solid films of an intermediate-length normal alkane, dotriacontane (n-C32H66), adsorbed onto a SiO2 surface. Our topographic and frictional images, recorded simultaneously in the contact mode, reveal a multilayer structure in which one to two layers of molecules adsorb adjacent to the SiO2 surface oriented with their long axis parallel to the interface followed by partial layers of molecules oriented perpendicular to the surface. The thicknesses of the parallel and perpendicular layers that we measured with the AFM agree with those inferred from previous x-ray specular reflectivity measurements on similarly prepared samples. We also observe bulk dotriacontane particles and, in contrast with our previous measurements, are able to determine their location. Above a minimum size, the bulk particles are separated from islands of perpendicularly oriented molecules by regions of exposed parallel layers that most likely extend underneath the particles. We find that the lateral friction is sensitive to the molecular orientation in the underlying crystalline film and can be used effectively with topographic measurements to resolve uncertainties in the film structure. We measure the same lateral friction on top of the bulk particles as on the perpendicular layers, a value that is about 2.5 times smaller than on a parallel layer. Scans on top of parallel layers indicate a constant height but reveal domains having different sublevels of friction. We explain this by the domains having different azimuthal orientations of the molecules.

Excitation of the shear horizontal mode in a monolayer by inelastic helium atom scattering.

Inelastic scattering of a low-energy atomic helium beam (HAS) by a physisorbed monolayer is treated in the one-phonon approximation using a time-dependent wave packet formulation. The calculations show that modes with shear horizontal polarization can be excited near high symmetry azimuths of the monolayer, in agreement with recent experiments. The parameters of the calculations are chosen to match the conditions of HAS experiments for triangular incommensurate monolayer solids of xenon, krypton, and argon adsorbed on the (111) face of platinum, and the results show many of the systematic experimental trends for relative excitation probability of the shear horizontal and longitudinal acoustic phonon branches. The inelastic scattering at beam energies near 8 meV is exceedingly sensitive to small misalignment between the scattering plane and the high symmetry directions of the monolayer solid. The diffraction and inelastic processes arise from a strong coupling of the incident atom to the target and the calculated results show large departures from expectations based on analogies to inelastic thermal neutron scattering.

Intramolecular diffusive motion in alkane monolayers studied by high-resolution quasielastic neutron scattering and molecular dynamics simulations.

Molecular dynamics simulations of a tetracosane (n-C24H50) monolayer adsorbed on a graphite basal-plane surface show that there are diffusive motions associated with the creation and annihilation of gauche defects occurring on a time scale of approximately 0.1-4 ns. We present evidence that these relatively slow motions are observable by high-energy-resolution quasielastic neutron scattering (QNS) thus demonstrating QNS as a technique, complementary to nuclear magnetic resonance, for studying conformational dynamics on a nanosecond time scale in molecular monolayers.

Mathematical model for in vitro drug release from controlled release dosage forms applied to propoxyphene hydrochloride pellets.

The in vitro release of drugs from controlled-release dosage forms has been studied in terms of a diffusion model. The model has been applied to a pellet formulation containing propoxyphene hydrochloride. It is demonstrated that the model may be used to predict the drug release profile adequately, when the pellet size is changed and when the thickness of the coating is varied. The size distribution of pellets in an experiment may be too broad to justify a simulation with just one average pellet size. Therefore, the results for pellets of the same size are generalized to any size distribution of pellets in an experiment. This is only trivial if sink condition exists in the extraction medium, since under that condition, the release from each pellet type is independent of the releases from other pellet types. In that case, the total release may therefore be found as the sum of the individual releases. In the general case considered here, the releases are coupled.